Microwave devices for wave guides of circular cross section



Nov. 15, 1960 E. A. .1. MARCATILI MICROWAVE DEVICES FOR WAVE GUIDES OFCIRCULAR CROSS SECTION Filed March 28, 1958 INVENTOR EJLJ. MARCAT/L/ BYATTORNEY 2,960,670 Patented Nov. 15, 1960 ilice MrcnowAv DEVICES ForWAVE GUIDES F CKRCULAR CROSS SECTION Enrique A. J. Marcati li, FairHaven, N.J., assignor to Bell Telephone Laboratories, Incorporated, NewYork, N.Y., a corporation of New York Filed Mar. 28, 1958, S e'i.1x61124324 8 Claims. Cl. 333-10 This invention relates toelectromagnetic wave transmission systems whose primary mode ofpropagation is the circular electric mode, and more particularly towaveguide components for use in such systems whose geometries areintrinsically compatible with'the circular electric modeto provideextraordinarily broad band operation directly in that mode.

The upper limit of the usable portion of the radio frequency spectrum iscontinually being raised in the effort to provide ever increasingnumbers of communication channels. The recognition that the circularelectric, TE mode propagating in metallic wave guides of circular crosssection has a loss characteristic inversely proportional to frequencypromises to substantially raise the frequency ceiling. As aconsequence,- the interest in circular wave guide theory and componentshas of late fluorished considerably. The breakthrough in componentsdevelopment has, however, been quite uneven. Since the transmissionmeans most often used in the propagation of energy through wa've guideshas been the rectangular wave guide supporting the dominant TE mode, andthe circular wave guide supporting the TE mode, most of the componentdevices required in these transmission systems are adapted to thesetypes of modes. The microwave art is replete with directional couplers,hybrids, circulators, isolators, frequency filters and the like, whosestructural geometries are peculiarly compatible with the electromagneticfield configuration of these modes of propagation.

This is not the case, however, with the circular electric modetvery fewcomponents have been developed which are intrinsically suited to thecircular electric mode. As a consequence, in order to perform thevarious operations upon the circular electric mode required in atransmission system it has been necessary to convert to the TE mode inrectangular pipe, or the TE mode in circular pipe. Microwave componentshave been developed to do this. For example, in United States Patent No.2,748,350, which was issued May 29, 1956, to S. E. Miller, there isdisclosed a directional coupler for dividing wave energy in any desiredproportion between the circular electric mode in a round guide and thedominant mode in arectangular guide, with the two guides disposedparallel to each other and sharing 'a common wall portion with couplingapertures therein. This directional coupler is excellent for itspurposes and has a band width of 20 percent. In' my copendingapplication, Serial No. 706,459, filed December 31, 1957, there aredisclosed channel dropping filters for extracting given frequency bandsfrom a round guide propagating the TE mode into a rectangular guidepropagating the TE' mode without introducing mode conversion in theprocess.

. It seerns clear, however, that at this early point in the developmentof the circular electric mode wave guide art the objective should be setfor developing microwave components intrinsically s'uited to thisinteresting and highly useful electromagnetic mode. Ultimately, it is tobe hoped that every operationthat is required'to be performed in acircular electric wave guide system will be performed directly upon thewave energy in the form of a circular electric mode without thenecessity for converting to some other mode merely because the microwavecomponent necessary to perform the needed function operates only in theother mode. It is to be expected that'bec'ause of the very specialnature and geometry'of the circularelectric mode field pattern, theordinary techniques and structures known in the art and applicable toother modes of propagation will be inadequate for providing guidance inthe creation of a class of microwave components peculiarly compatiblewith the circular electric mode.

One very important operation in any microwave transmission system isthat of transferring energy'from one transmission line to' another,either completely, or in various desired ratios, for the purpose, forexample, of sampling energy from the main transmission path, orintroducing wave energy into the main transmission path from a repeaterstation or for abstracting energy from the main transmission path intothe repeater.

It is the primary object ofthis' invention to provide directionalcoupling between two transmission lines each of which supports energysolely in a circular electric mode.

In accordance with the invention, this object is accomplished by adirectional coupler whose geometry is related to the geometry of thecircular electric mode field pattern in a manner whichis peculiarlyconsonant and conguent therewith. Specifically, a circular wave guidehas a gap interrupting its longitudinally extending conductive boundary.Adjacent ends of the wave guide define the longitudinal extent, d, ofthe gap. The guide is proportioned to' support solely the lowestnumbered circular electric mode, namely the TE Coaxial with andcircumscribing the round guide in the region of the gap is a secondround guide proportioned to support both the TE and the TE modes, butnoother higher numbered circular electric rnode'. Wave energy propagating through the internal coaxial guide, upon reaching the gap, will'excite in the outside coaxial guide in' the region of the gap both theTEM and the TE modes, both ofwhich the external guide is proportioned tosupport. Since, as is well known-in the'art, these twomodes propagatewith different phase velocities, the phase relationship between the twomodes will vary with distance. This results in a power division betweenthe internal giiide and the external guide at the end of the gap, theratio of which is dependent upon the length d. Thus, for example, if dis equal to an odd number of one-quarter beat wavelengths there will bean equal division between wave guides; if d is one-half a beatWavelength there will be a complete power transfer from the internalguide to the external guide; while if dis a whole beat wavelength theenergy will continue propagating completely within the internal guide onthe other side of the gap. It is clear, therefore, that any desireddivision of power may be obtained by the appropriate choice of thelength d relative to the difference between the phase velocities ofthe'two modes. In this way directional coupling is obtained without theinefli'cient expedient of converting to some other mode incongruent ordissimilar to that of the circular electric type.

At this point in the development of the circular electric mode art,however, it is highly probable that the transferred energy would have tobe converted into the dominant mode in a rectangular guide to beefiectively utilized, e.g., demodulated, amplified, filtered or thelike. This'conversion,however, may bedone in.a manner well known in theart and will be described in greater detail below.

Nevertheless, the fact that directional coupling is performed, inaccordance with the invention, exclusively in the circular electric modehas very important consequences. Firstly, this is a contribution to anemerging development of an entire class of microwave componentsintrinsically and efiiciently operative in the circular electric mode.Secondly, by proportioning the external wave guide so that it is justbelow cut-off for the TE mode in the operating frequency range and byproportioning the internal guide so that its conductive boundarycoincides with the electric field null of the TE mode supported by theexternal guide, the directional coupler will be operating at frequenciesconsiderably removed from cutoff. Since a directional coupler becomesless frequency sensitive with removal of the operating range fromcutoff, it is clear that this device is very broad band; indeedfrequency bands as great as 40 percent may theoretically be transferredbetween transmission lines in this way. Whether this theoretical bandlimit may be achieved in actuality has not been determined since thereis no microwave generator known in the art which is sutficiently broadband to test the limits of the device at the mid-band frequencies ofinterest, i.e., the millimeter wave region.

A feature peculiar to the directional coupler in accordance with theinvention, is that no matching elements are needed to eliminatereflections in the region where the energy is divided between theinternal and external coaxial guides because the structural geometry ofthe power divider is intrinsically consonant with the geometry of theelectric field patterns of the TE and TE modes in round guides.

Other objects and certain features and advantages of the invention willbecome apparent during the course of the following detailed descriptionof the specific illustrative embodiments of the invention shown in theaccom panying drawings.

In the drawings:

Fig. 1 is a perspective cutaway view of an embodiment of a directionalcoupler for circular electric modes given by way of example, inaccordance with the invention;

Figs. 2a, 2b, 3a, 3b, are representative curves and models, given by wayof explanation, of certain mode field patterns helpful for anunderstanding of the operation of the embodiment of Fig. l; and

Figs. 4a through 4e are successive transverse cross-sectional views of amode transducer utilized in the embodiment of Fig. 1.

In more detail, Fig. l is a perspective view of a directional coupler inaccordance with the invention whose structural geometry is compatiblewith that of the field pattern of the circular electric mode. Fig. 1 maybe conveniently considered as comprising two major sections; the firstis the directional coupler itself; the second is a transducer forabstracting wave energy from one port of the directional coupler and forconverting it into dominant mode wave energy in rectangular guide.

Considering now the first section, namely the directional coupleritself, there are disclosed two lengths 11 and 12 of hollow conductivewave guide having a circular transverse cross section, each of which isproportioned to support the circular electric TE mode to the exclusionof all the higher numbered circular electric modes. Guides 11 and 12 areof the same transverse dimensions and are colinearly disposed inlongitudinal succession with adjacent ends spaced from each other by adistance d to form a coupling gap 10. Surrounding guides 11 and 12, andcoaxially disposed with respect to each of them is a hollow conductivewave guide 13 of circular cross section providing a conductive boundaryaround both said guides 11 and 12 and around gap 10. Guide 13 in theregion of gap is proportioned to support both the .TE and the TEcircular electric modes, to the exclusion of all higher numberedcircular electric modes, and

its radius r is related to to the radii r, of guides 11 and 12 in aspecial manner to be discussed in greater detail below. Supporting eachof guides 11 and 12 in their coaxial positions within guide 13 arehollow dielectric cylinders or washers 14 and 15 circumscribing guides11 and 12 and otherwise completely filling guide 13, in a manner wellknown in the coaxial conductor art. Washers 14 and 15 are preferablymade of dielectric material having a very low dielectric constant, suchas polyfoam, so as to minimize the possibility of reflection of waveenergy incident thereon. For ease of reference, the four ports of thedirectional coupler are designated as follows: Port 1 is guide 11; port2 is the ring-like region between guide 12 and the internal boundary ofguide 13; port 3 is guide 12; and port 4 is the ring-like region betweenguide 11 and the internal boundary of guide 13. The operation of thedirectional coupler thus described, and certain other structuralrelationships in this device, may more readily be understood byconsidering certain characteristics of the circular electric modes whichwill now briefly be reviewed, but only to the extent necessary tofacilitate a comprehension of the structure of Fig. l.

The circular electric modes are in general designated TE The TE,representing transverse electric, indicates that the electric fieldcomponents are everywhere directed exclusively transverse to thelongitudinal axis of the wave guide and the direction of propagation ofwave energy therethrough. The O designation represents the order andnumber respectively, of this family of modes. The order is zero in everycase to indicate the number of whole periods of the transverse electriccomponent encountered in passing around the circumference of the crosssection of the guide. On the other hand, n represents the number of halfperiods encountered in passing along the radius of the wave guide crosssection. Examples of the field patterns of the TE and TE modes in atransverse cross section of a round wave guide will serve to illustratethese designations and also demonstrate the electric fieldconfigurations of the two modes of interest in the embodiment of Fig. 1.

Fig. 2a represents the TE mode. In accordance with the above designationit can be seen that in passing around the circumference of the guide thepolarity of the electric field components (the solid concentric circles)is nowhere reversed and thus there is no whole period represented, whilein passing from the center of the guide to the circumference along theradius, it can be seen that the polarity remains constant and thus onlyonehalf period is represented. Fig. 2b is another type of representationof the electric field pattern of the TE mode which is well known in theart. The ordinate represents the intensity of the field pattern, whilethe abscissa represents distance from the center of the wave guide (thisis merely another form representative of the electric field pattern ofFig. 2a). In Fig. 3a the TE mode is represented; it may be seen that inpassing from the center of the guide to the circumference along theradius there is a reversal in the polarity of the electric fieldcomponents (and thus an electric field null exists), justifying thedesignation of this field configuration as the second numbered circularelectric mode. Fig. 3b is the other type of representation of theelectric field pattern of the TE mode.

As is Well known in the art every electromagnetic mode, at a givenfrequency, requires a wave guide of a certain minimum transversedimension in order for it to be propagated. Conversely a round waveguide of a given radius will support only those frequencies, in theparticular mode of interest, which are above a certain minimum frequency(whose wavelength is known as the cut-off wavelength). Lowerfrequencies, having larger wavelengths, will not be supported by thewave guide. Parametric expressions relating the cut-off wavelength, theradius of the circular wave guide, and a function of the electromagneticmode, are well known in the art.

vThus, itis known that the cut-01f wavelength for'the TE03 mode is forthe TE mode and for the TE mode where h is the cut-off wavelength, r isthe radius of the wave guide, and the denominator in each instance isthe appropriate Bessel function root for the particular transverseelectric mode involved. Fora more complete description of this subject,reference may be had to any standard textbook on the subject, such asPrinciples and Applications of Waveguide Transmission 'by G. C.Southworth, D. Van Nostrand and=Col, pages 119 through 129. Keeping theoperating frequency -.range in mind, it is therefore relatively simplewith :these parametric relationships :to design the wave guides 11, 12and 13 .in accordance with the requirements specified above. Thus theradius, r of external guide 13 may be selected such that guide 13 isjust below cut-off in the region of gap for the TE mode at the highestfrequency in the operating range. Radii, r of the internal guides 11 and12 are then readily determined so that the conductive boundaries ofguides 11 and 12 coincide with the electric field null of the TE mode(see Figs. 3a and 3b) supported in the external guide '13 along couplinggap 10, i.e., with r determined, r, is equal to r multiplied by theratio of theBessel function constants of the TE and TE modes;

. thus In this way the directional coupler of Fig. 1 will be operativein a frequency range substantially removed from the cut-off wavelength.and will benefit as a result by the relative frequency insensitivecharacteristic of .this

type of operation. 7

The operation of the directional coupler of Fig. 1 may now properly becomprehended with the aid of the field patterns disclosed in Figs. 2athrough 3b. Electromagnetic wave energy is exited at the left-hand endof guide 11 exclusively in the TE mode. This energy propagates to theright along guide 11 until itreaches coupling gap 10. Immediately uponentering gap 10,

wherein both the TE and TE modes may 'be supported, the wave energycomprises both these modes. The electric field pattern thereforeimmediately at the left-hand end of gap 10 may be considered as asuperposition of the TE ielectric field pattern, as represented tion ofguide 12 at unequal velocities. Accordingly, the

phase relationship of the twomodes changes, of. necessity, alongthedistance d of coupling gap 10. If distance d is selected such that thedirectional coupler is arranged :to provide a complete transfer fromport -1 to port 2, the electric vectors of the two modes at the end ofthe gap near. guide 12 willbe in phaseiwithin the ring-like transversearea corresponding to port,2, but will beoppositely phased in thetransverse area corresponding to port 3. Accordingly, port2 will beexcited by the energy which initally entered guide 11. Furthermore, theelectric field pattern exciting port 2 and propagating down guide 13external to guide 12 will be of the TE type but now, of course, in acoaxial wave guide. In this discussion the phase relationships betweenthe .electric field patterns of the TE and TE modes in the couplingprocess have been described. Amplitude relationships are also involved.This latter part of the theory of the device of Fig. 1 does not howeverlend itself to a simple qualitative description. Computation of thecontributions of a multiplicity of modes, .many of which are belowcut-01f, in addition to the T13 and TE modes must be made in order topresent a quantitatively accurate description; i.e. nothing less than asolution of Maxwells equation for the boundary conditions of theembodiment of Fig. 1 is needed. This theoretical analysis will not bepresented since the structure of the invention would not be betterunderstood thereby, and it is a straightforward, albeit laborious,process for one skilled in the art.

It may be noted that in the arrangement of the embodiment of theinvention wherein the energy is coupled completely from port 1 to port2, the phase relationship between the two modes at the right-hand end ofgap 10 is :exactly 180 degrees out-of-phase from what it was at thebeginning of the coupling region, i.e.

where [3 is the phase constant of the TE mode, [3 the phase constant ofthe TE mode, and n is in integer. Were it desired to provide equal powerdivision between ports 2 and 3, the distance d could be changed (to anodd number of one-quarter beat wavelengths rather than an odd integralnumber of one-half beat wavelengths) so that the phase relationshipsbetween the modes at the right-hand end of gap 10 is exactly degreesdifferent from what it was at the beginning of the coupling region,i.e.,

It can'be seen, therefore, that any ratio of power transfer desired maybe readily accomplished byappropriately fixing the distance d.

It is clear that in theoperation of the directional coupler the TE modeis readily matched to ports 2 and 3 since the conductive'boundary ofguide 12 is designed, as was explained above, to coincide precisely withthe electric field null of this mode. It is not so apparent,however,'that the TE mode is matched since it would appear that theconductive boundary of guide 12 coincides with a region where theelectric field of't'his modelhas'a finite value. It is the case that inany multimode waveguide, the amount of wave energy scattered forwardfrom an impedance discontinuity is far in excess 'of the amountreflected. Actually, a scattering matrix presentedin standard works, forexample, Waveguide Handbookiby Marcuvitz, Radiation Laboratory Series,volume 10, 1951, pages 106 through 108, and The Use of ScatteringMatrices in Microwave Circuits, by Mat- -thews,I.R.E. Transactions onMicrowave Theory and Techniques, April 1955, page 21. That reflectionsfrom the coupler are in fact negligible is well borne out by the dataobtained from several successful reductions to practice of the inventionin accordance with Fig. 1. Thus in couplers operating over a frequencyrange from 50.4 kmc. to 60.6 kmc., wherein guide 13 had an internaldiameter of 0.649 inch, guides 11 and 12 had internal diameters of 0.354inch and the coupling gap length d had values of 0.226, 0.452, and 0.906inch to provide equal power division between ports 2 and 3, completepower transfer, and no transfer, respectively, the largest reflectedsignal over the entire frequency band in all three cases Was down 23decibels below the incoming signal. It is of considerable interest tonote that there were absolutely no heat losses due to the directionalcoupler.

Considering the embodiment of Fig. 1 again, we might consider how tomake the energy transferred to port 2 available for subsequent use. Thisis readily accomplished in manner well known in the art and constitutesthe second section of the embodiment of Fig. 1 mentioned above. Thedevice to the right of the directional coupler is a transducer forconverting the coaxial TE mode propagating from port 2 between guides 12and 13 into the dominant mode in a rectangular wave guide 16. This is inessence a mode converter of the type disclosed in G. C. Southworths bookmentioned above, at page 363. The converter progressively varies thetransverse shape of the double pipe coaxial guide such that the boundarybetween guides 12 and 13 is gradally tapered to a rectangular crosssection as indicated by Figs. 4a through 4e of the drawings. In this waythe TE coaxial mode is gradually deformed into the TE dominant mode tocontinue propagating along the rectangular guide 16 to the right, to beutilized as desired with standard techniques.

Such a mode converter may also be utilized at the other end of thedirectional coupler so that energy entering guide 12 from the rightwould be transferred from port 3 to port 4 and could thence be taken outby a wave converter of the type represented by Figs. 4a through 4e. Anarrangement such as this would also be useful in a long distance waveguide system. Wave energy from the long distance circular wave guide 11could be transferred through port 2 to rectangular guide 16 and thenceto a repeater station (not shown) for proper amplification, timing,modulation and the like, and could be reintroduced into the wave guidesystem by means of the wave converter to the left of the directionalcoupler discussed above (not shown) and thence from port 4 to port 3 forcontinued propagation along long distance guide 12.

In all cases, it is to be understood that the abovedescribedarrangements are simply illustrative of a small number of the manypossible specific embodiments which represent applications of theprinciples of the invention. Numerous and varied other arrangements canreadily be devised in accordance with these principles by those skilledin the art Without departing from the spirit and scope of the invention.

What is claimed is:

1. A multiple port wave guide coupling apparatus for electromagneticwave energy in circular electric wave modes comprising first and secondsimilar sections of hollow conductive wave guide extending collinearlyin longitudinal succession with adjacent ends of said sections spacedapart a given distance to form a gap in the conductive boundary formedby said sections, said first and second guide sections forming first andthird ports of said said coupling apparatus, a third section of hollowconductive wave guide disposed external to and coaxial with at least aportion of each of said first and second guide sections to provide aconductive boundary surrounding said gap, the regions between said firstand third guide sections and between said second and third guidesections forming second and fourth ports of said coupling apparatus, andmeans for applying electromagnetic waves in a hollow pipe wave mode toone of said ports, said third guide section having a cut-0E determiningdimension k proportioned to support first and second distinct hollowpipe wave modes in the region of said gap at the frequency of theapplied waves, said first and second guide sections having cut-offdetermining dimensions k proportioned to support said first mode to theexclusion of said second mode at said frequency, said cut-offdetermining dimensions being related by the expression where 1,, and Iare the Bessel function constants associated with said first and secondmodes.

2. A combination as recited in claim 1 wherein said first and secondmodes have different phase constants.

3. A combination as recited in claim 1 wherein said first, second andthird guide sections have circular transverse cross sections, said firstmode is the TE circular electric mode and said second mode is the TEcircular electric mode.

4. A combination as recited in claim 3 wherein said third guide sectionis proportioned to be slightly below cut-off for the TE mode forfrequencies within said range.

5. Coupling apparatus for electromagnetic wave energy in circularelectric modal field configurations comprising first and second sectionsof hollow pipe wave guide adapted to propagate traveling waves in hollowpipe wave modes therethrough at microwave frequencies, said sectionshaving substantially identical circular transverse cross sections within side radii r, and being spaced apart on a common longitudinal axis toform a gap between adjacent end portions thereof, the nonadjacent endportions of said sections forming first and third terminals of saidapparatus, a third section of hollow pipe wave guide of circulartransverse cross section with inside radius r surrounding said gap andat least a portion of each of said first and said second guide sections,the regions between said first and third guides and between said secondand third guides forming transmission paths for waves coupled from saidgap and also forming second and fourth terminals of said apparatus, saidradii r, and r being related by I TE JTEO(D+1) so that said third guidesupports first and second distinct hollow pipe wave modes at frequencieswithin the operating range and said first and second guide sectionssupport said first mode to the exclusion of said second mode in saidfrequency range, Where JTEOD and JTEMMD are the Bessel functionconstants for said first and second modes respectively.

6. Coupling apparatus according to claim 5 in which said first mode isthe TE circular electric mode and said second mode is the TE circularelectric mode.

7. Apparatus according to claim 5 in which said third wave guide isproportioned to be slightly below cut-off for the TEO( +2) mode in saidfrequency range.

8. In combination, a section of hollow pipe wave guide having first andsecond ends and having a circular transverse cross section with a radiusr, greater than 0.3 free space wavelength of the lowest frequency wavesto be transmitted but proportioned to be below cut-off for all circularelectric Wave modes except the TE mode for frequencies within theoperating range, a second section of hollow pipe wave guide similar tosaid first guide section longitudinally adjacent said first section withadjacent ends of said first and second section spaced away to form agap, and a third guide section having a circular transverse crosssection with a radius r equal to 1.83m

coaxially disposed about said second section and extending at least tothe end of said first section which defines said gap, means for excitingsaid first section in the TE Wave mode at the end distant from said gap,and means for receiving energy coupled at said gap at the end of saidsecond section distant from said gap and at the end of said thirdsection distant form said gap.

References Cited in the file of this patent UNITED STATES PATENTS WalkerOct. 22, 1957

